Відео

I can get behind this perspective for sure. You're basically saying that in the sentence 'I add 3 and 4' the verb 'add' is more about the calculation action than the calculation content, and 'and' is really the part that's doing the 'content' of the calculation. Is that right? Regarding our brains being better at infix. I think there's probably some truth to that, but we also can never untangle our experience with learning it that way from a young age. Classic nature vs nurture, eh?

Interesting idea!

You make some good points for sure! If we had adopted prefix or postfix then conventions like how we go about writing equality may have developed differently too. But we definitely have optimized everything for infix. Either way the purpose of the video was more a small footnote on the main topic I introduced previously meant to connect prefix with VO and postfix with OV. Thanks for watching and the insights ^^

I thought so too!

kragkruger1127! 🤩

Great point. In many ways prefix notation is kind of like a precursor to thinking in terms of functions! (And also operations can be viewed as functions in their own right, for example + is a function with two inputs (namely the operands you add together)).

Alive and well

🎉🎉🎉

Thank you! For how my videos were doing at the time (10-30 views/video) it kinda did feel like it went viral for me 😅

You were featured in spirit

Pfizer? More like Beau Mathszer

Bone Maths

Good

Everest baby

And we’re just getting started 🔥

Thank YOU

Groove check ✅

Excellent observation! There’s actually a reason for this. Applying a reciprocal and applying a negative are examples of what are called inverse elements. Applying a - gives what’s called the additive inverse and applying a reciprocal gives what’s called the multiplicative inverse. And we actually go into extensive depth on these ideas in FOA 47 so I recommend you go check that out!

@@beaumaths just watched it, I see what you mean!

That’s the Beau Maths difference baby

I plan to!

Indeed

That’s the Beau Maths difference

Thank you!

Yeah associativity is one property that allows for us to rearrange these trees

Atta boy 🔥🔥🔥🔥

You’ll come scurrying on back in no time

We can do a whole series on card counting with that

Thanks! 100 subscriber video coming within the next 2-3 weeks

Glad someone remembered parenthesis appreciation day. Stand-Up Maths collab at 3051 subscribers?????

Thanks~ Visual methods like trees are always a great perspective to have, indeed!

Indeed

He would’ve learned this there then

Stay safe out there

That’s because it is

Thanks!

Great point! This is actually something I'm going to discuss in the exercise video. This leads to a subtlety on if we are considering exponentiation to be a unary operation (for example, 3^2 as being applying the operation 'power of 2' to the number 3) or as a binary operation (for example, 3^2 as being an operation that combines the numbers 3 and 2). If we think of it as a unary operation we run into the well-definedness issue discussed. If we think of it as a binary operation, we can do as you suggest. For most purposes, granted, we can somewhat freely think about exponentiation in either way.

Also in PEDMAS 3^5^2 would be standardly evaluated as 3^25 since we focus on the exponent first. And the exponent of 3 is the 5^2, so we evaluate everything in there. And then we get 3^25. You can think about it as having an implicit set of parenthesis in the exponent grouping everything in there that must be evaluated before we actually take the exponent. For example if in the power of the 3 I wrote 2+2x3, I would be basically writing 3^(2+2x3) where I evaluate 2+2x3 to be 8 and then doing 3^8 to get my result.

@@beaumathsthere is no reason to treat exponentiation as a unary operation, since it just isn't one

Exponentiation is a binary operation, I agree. However, if we fix the power, we can regard it as a unary operation. 3^2, 4^2, 8^2 can all be thought of as me applying this “power of 2” unary operation to each of 3, 4, and 8. Since the power is fixed at 2, it isn’t something we have the ability to change and thus isn’t an input, making it a unary operation

@@beaumaths But that can be done with _any_ binary operation, so it's not particularly useful to do it with only one of them. ( also if you do it as a unary operator, you'd have to make a unary operator ^x the result of which depends on more than just the operand, which is not how operators work by any reasonable definition ) And in normal math exponentiation is treated like a function anyway, so if you follow with that, its precedence cannot be changed since it has none. It'd just get evaluated first. And you can't not follow that if you want the behaviour of inverse operations to be consistent unless you want to turn logarithms into an operator, which i guess is reasonable but also is cursed.

By evaluating brackets last, they essentially become an operation that does nothing. So with EDMASB it would be impossible to model all types of expressions. Since there’s no longer an operation that groups things, there is no way around evaluating the expression with this given order of operations. For example, it would be impossible to ever get an expression where addition is evaluated before multiplication because it comes after multiplication here and we have no brackets to prioritize addition